%0 Journal Article %1 marcus13 %A Marcus, Adam %A Spielman, Daniel A %A Srivastava, Nikhil %D 2013 %K cauchy.binet characteristic determinant interlacing kadison.singer multilinear multivariate polynomial real-rooted root root-free stable %T Interlacing Families II: Mixed Characteristic Polynomials and the Kadison-Singer Problem %U http://arxiv.org/abs/1306.3969 %X We use the method of interlacing families of polynomials to prove Weaver's conjecture KS2, which is known to imply a positive solution to the Kadison-Singer problem via a projection paving conjecture of Akemann and Anderson. Our proof goes through an analysis of the largest roots of a family of polynomials that we call the "mixed characteristic polynomials" of a collection of matrices.

@article{marcus13, abstract = {We use the method of interlacing families of polynomials to prove Weaver's conjecture KS2, which is known to imply a positive solution to the Kadison-Singer problem via a projection paving conjecture of Akemann and Anderson. Our proof goes through an analysis of the largest roots of a family of polynomials that we call the "mixed characteristic polynomials" of a collection of matrices.}, added-at = {2014-01-24T18:00:14.000+0100}, archiveprefix = {arXiv}, author = {Marcus, Adam and Spielman, Daniel A and Srivastava, Nikhil}, biburl = {https://www.bibsonomy.org/bibtex/24598494915a1952abc928e12e3f68f7c/ytyoun}, eprint = {1306.3969}, interhash = {086a38355c8dbaca629fb57788d67edc}, intrahash = {4598494915a1952abc928e12e3f68f7c}, keywords = {cauchy.binet characteristic determinant interlacing kadison.singer multilinear multivariate polynomial real-rooted root root-free stable}, primaryclass = {math.CO}, timestamp = {2017-12-10T08:36:11.000+0100}, title = {Interlacing Families {II}: Mixed Characteristic Polynomials and the {Kadison-Singer} Problem}, url = {http://arxiv.org/abs/1306.3969}, year = 2013 }